The value of x to the nearest tenth is:

Question

If (0.2)^x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:

(a) -10.0, (b) -0.5, (c) -0.4, (d) -0.2, (e) 10.0

Answer 1

The equation

(0.2)^x   =   2

Apply lolgorithm to each side

log (0.2)^x   =   log 2

x [log (0.2) ]   =   0.3010                   [Since log 2 =  0.3010]

x [ log (2/10) ]   =   0.3010

x [ log 2 - log 10 ]   =   0.3010

x [ - 0.699 ]   =   0.3010

x [ 0.3010 - 1 ]   =   0.3010

x    =   0.3010/ (-0.699}

x  =  - 0.430

x  =  - 0.4              [The value of 'x' to the nearest tenth]

Ans : Option 'c'